# How do you rationalize the denominator and simplify #(4+sqrt3)/(5+sqrt2)#?

To rationalize the denominator we must get rid of any radicals in the denominator.

We can rationalize the denominator of a binomial by multiplying the numerator and the denominator by the conjugate of the denominator.

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To rationalize the denominator and simplify (4+sqrt3)/(5+sqrt2), we multiply both the numerator and denominator by the conjugate of the denominator, which is (5-sqrt2). This results in (4+sqrt3)(5-sqrt2) in the numerator and (5+sqrt2)(5-sqrt2) in the denominator. Expanding and simplifying these expressions gives (20-4sqrt2+5sqrt3-sqrt6) in the numerator and (25-2) in the denominator. Combining like terms, the simplified expression is (18+5sqrt3-4sqrt2-sqrt6)/23.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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